An OR team has created the following Linear Programming model to help the company make some executive decisions on the number of batches of each type of broom (x1 and x2) to be made per cycle: Max 10x1 + 20x2 s.t. 3 x1 + 4 x2 31 x1 5 -5 x1 + 6 x2 18 and x1 0 , x2 0

a) Use graphical method to solve the problem.

b) Find range of optimality for c1 and c2

c) What is dual price for s1 ?

d) Suppose that a mistake was made but nothing needed to be changed in the program except for the objective, which should now be 20x1 + 10x2. Please determine if the optimal solution has changed and find the new value of z.

e) Suppose that the original model was correct. Propose an objective function for which the problem has multiple solutions. Be sure to graph the new objective function and to point out the optimal solutions on your graph.

f) Suppose the constraint 3 x1 + 4 x2 31 needs to be changed to equality: 3 x1 + 4 x2 = 31. What will be the optimal solution now?